Search Results for: the-moment-of-proof-mathematical-epiphanies

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'Rarely does one come across a mathematics book with such breadth and insight. Dr. Benson's book contains valuable information--not only for curious students and laypeople --but also for seasoned researchers. Particularly fascinating is the curious range of topics, from fractals and fiendishly difficult games to the mathematics of precariously-leaning brick towers! All the topics are sure to stimulate readers' imagination and sense of wonder at the incredible vastness of our mathematical universe.' --Dr. Clifford Pickover, author of Time: A Traveler's Guide'A useful book, offering a rich collection of interesting and enjoyable mathematics.' --Reuben Hersh, author of What is Mathematics, Really?'Donald Benson shows what mathematicians mean when they speak of the beauty of mathematics -- an artistic beauty of logical elegance and occasionally surprise.' --Keith Devlin, author of The Language of Mathematics: Making the Invisible Visible and Life by the Numbers

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This book takes a novel look at the topics of school mathematics--arithmetic, geometry, algebra, and calculus. In this stroll on the mathematical seashore we hope to find, quoting Newton, "...a smoother pebble or a prettier shell than ordinary..." This book assembles a collection of mathematical pebbles that are important as well as beautiful.

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"Humans are the only animals who create and solve puzzles—for the sheer pleasure of it—and there is no obvious genetic reason why we would do this. Marcel Danesi explores the psychology of puzzles and puzzling, with scores of classic examples. His pioneering book is both entertaining and enlightening." —Will Shortz, Crossword Editor, The New York Times "... Puzzle fanatics will enjoy the many riddles, illusions, cryptograms and other mind-benders offered for analysis." —Psychology Today "... a bristlingly clear... always intriguing survey of the history and rationale of puzzles.... [A] splendid study...." —Knight Ridder Newspapers

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The Ballet of the Planets unravels the beautiful mystery of planetary motion, revealing how our understanding of astronomy evolved from Archimedes and Ptolemy to Copernicus, Kepler, and Newton. Mathematician Donald Benson shows that ancient theories of planetary motion were based on the assumptions that the Earth was the center of the universe and the planets moved in a uniform circular motion. Since ancient astronomers noted that occasionally a planet would exhibit retrograde motion--would seem to reverse its direction and move briefly westward--they concluded that the planets moved in epicyclic curves, circles with smaller interior loops, similar to the patterns of a child's Spirograph. With the coming of the Copernican revolution, the retrograde motion was seen to be apparent rather than real, leading to the idea that the planets moved in ellipses. This laid the ground for Newton's great achievement--integrating the concepts of astronomy and mechanics--which revealed not only how the planets moved, but also why. Throughout, Benson focuses on naked-eye astronomy, which makes it easy for the novice to grasp the work of these pioneers of astronomy.

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Draws on expertise from psychology, neurology and evolutionary psychology to illuminate the process of spontaneous flashes of human insight, surveying engaging examples from the fields of religion, science, math and art.

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With a foreword by Tim Rice, this book will change the way you see the world. Why is it better to buy a lottery ticket on a Friday? Why are showers always too hot or too cold? And what's the connection between a rugby player taking a conversion and a tourist trying to get the best photograph of Nelson's Column? These and many other fascinating questions are answered in this entertaining and highly informative book, which is ideal for anyone wanting to remind themselves or discover for the first time that maths is relevant to almost everything we do. Dating, cooking, travelling by car, gambling and even life-saving techniques have links with intriguing mathematical problems, as you will find explained here. Whether you have a PhD in astrophysics or haven't touched a maths problem since your school days, this book will give you a fresh understanding of the world around you.

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This inexpensive paperback uses lively language to put mathematics in an interesting, historical context and points out the many links to art, philosophy, music, computers, navigation, science, and technology. The arithmetic, algebra, and geometry are presented in a way that makes them relevant to daily life as well as larger issues. Topics include: Oh So Mysterious Egyptian Mathematics; Mesopotamia Here We Come; Those Incredible Greeks; Greeks Bearing Gifts; Must All Good Things Come to an End?; Europe Smells the Coffee; Mathematics Marches On; A Few Good Men; A Most Amazing Century of Mathematical Marvels!; The Age of Euler; A Century of Surprises; Ones and Zeros; Some More Math Before You Go.

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Mathematician Ian Stewart tells readers what he wishes he had known when he was a student. He takes up subjects ranging from the philosophical to the practical-what mathematics is and why it’s worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others.

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This new series offers the most comprehensive views of key areas in the world of science. Each set explores all facets of the topic, offering not only descriptive and analytical information, but also cultural and ethical issues, and career opportunities in many fields of science.

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A walk through history's most mind-boggling puzzles Ever since the Sphinx asked his legendary riddle of Oedipus, riddles, conundrums, and puzzles of all sizes have kept humankind perplexed and amused. The Liar Paradox and the Towers of Hanoi takes die-hard puzzle mavens on a tour of the world's most enduringly intriguing braintwisters, from KÃ¶nigsberg's Bridges and the Hanoi Towers to Fibonacci's Rabbits, the Four Color Problem, and the Magic Square. Each chapter introduces the basic puzzle, discusses the mathematics behind it, and includes exercises and answers plus additional puzzles similar to the one under discussion. Here is a veritable kaleidoscope of puzzling labyrinths, maps, bridges, and optical illusions that will keep aficionados entertained for hours. Marcel Danesi (Etobicoke, ON, Canada) is the author of Increase Your Puzzle IQ

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This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

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This up-to-date resource presents 3,500 national, regional, local and international lists and rankings compiled from hundreds of sources. Entries typically include a description of the ranking; background information on criteria for establishing the hierarchy; additional remarks about the ranking; the complete or partial (if extensive) ranking; and a complete source citation for locating additional information if necessary.